Coverage for local/lib/python2.7/site-packages/sage/quadratic_forms/quadratic_form__mass.py : 33%
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""" Shimura Mass """ ###################################################### ## Routines to compute the mass of a quadratic form ## ######################################################
## Import all general mass finding routines from sage.quadratic_forms.quadratic_form__mass__Siegel_densities import \ mass__by_Siegel_densities, \ Pall_mass_density_at_odd_prime, \ Watson_mass_at_2, \ Kitaoka_mass_at_2, \ mass_at_two_by_counting_mod_power from sage.quadratic_forms.quadratic_form__mass__Conway_Sloane_masses import \ parity, \ is_even, \ is_odd, \ conway_species_list_at_odd_prime, \ conway_species_list_at_2, \ conway_octane_of_this_unimodular_Jordan_block_at_2, \ conway_diagonal_factor, \ conway_cross_product_doubled_power, \ conway_type_factor, \ conway_p_mass, \ conway_standard_p_mass, \ conway_standard_mass, \ conway_mass # conway_generic_mass, \ # conway_p_mass_adjustment
###################################################
def shimura_mass__maximal(self,): """ Use Shimura's exact mass formula to compute the mass of a maximal quadratic lattice. This works for any totally real number field, but has a small technical restriction when `n` is odd.
INPUT:
none
OUTPUT:
a rational number
EXAMPLES::
sage: Q = DiagonalQuadraticForm(ZZ, [1,1,1]) sage: Q.shimura_mass__maximal()
"""
def GHY_mass__maximal(self): """ Use the GHY formula to compute the mass of a (maximal?) quadratic lattice. This works for any number field.
Reference: See [GHY, Prop 7.4 and 7.5, p121] and [GY, Thrm 10.20, p25].
INPUT:
none
OUTPUT:
a rational number
EXAMPLES::
sage: Q = DiagonalQuadraticForm(ZZ, [1,1,1]) sage: Q.GHY_mass__maximal()
""" |